CN103064071A - Radar target attribute scattering center feature extraction method based on sparse decomposition - Google Patents

Abstract

The invention discloses a radar target attribute scattering center feature extraction method based on sparse decomposition. The radar target attribute scattering center feature extraction method based on the sparse decomposition mainly solves the problems in an existing method capable of segmenting an image to extract attribute scattering center based on the radar image that models are unmatched, features are easy to lose, and parameter estimation accuracy is low. The implementation process includes the following steps: building a scattering center intensity threshold by using noise samples, conducting an intensive scattering center test in the radar image and confirming a values set of a scattering center parameter, obtaining a target attribute scattering center parameter super-resolution estimation set according to attribute scattering center models by using coordinate repeated decline technology to build a super-resolution dictionary through solving the problem of 0 norm optimization, and extracting geometric dimensioning features of the target and important components of the target according to the scattering center parameter set. The radar target attribute scattering center feature extraction method based on the sparse decomposition is capable of effectively extracting the target attribute scattering center and the super-resolution scattering center parameter, accurately estimating the geometric dimensioning features of the target and the important components of the target, and can be used for radar target classification and identification.

Description

Radar target attribute scattering center feature extracting method based on Its Sparse Decomposition

Technical field

The invention belongs to the Radar Technology field, relate to a kind of radar target attribute scattering center feature extracting method, can be used for the physical dimension of estimating target and vitals thereof, for target classification identification provides important characteristic information.

Background technology

The radar imagery technology is to grow up the 1950's, and radar image is the two-dimensional scattering figure of target.The tradition radar imagery is take the point scattering model as the basis, and this model only comprises the target scattering dot position information, but only utilize the recognition feature of the positional information structure of target scattering point can not complete sign radar image in the essential attribute of target.In optical zone, the high-frequency electromagnetic scattering response of expansion target can be with the scatterer of one group of independent distribution, or the electromagnetic scattering response sum approximate representation of title scattering center.The scattering center of target mainly results from the point of discontinuity positions such as edge, flex point, corner angle and tip of target, represented the meticulous physical arrangement of target, so scattering center model can more relevantly be described objective attribute target attribute, also in the radar target recognition field important application is arranged.

Based on geometric theory of diffraction and physical optics theory, Michael J.Gerry in 1999 and Lee C.Potter have proposed the parameterized model that is applicable to synthetic-aperture radar (SAR)-attribute scattering center model, see [M.J.Gerry, L.C.Potter, I.J.Gupta, and A.van der Merwe, A parametric model for syntheticaperture radar measurements[J] .IEEE Transactions on Antennas and Propagation, 1999, Vol.47, NO.7, pp.1179-1188].The attribute scattering center model is with position, shape, direction and the amplitude etc. of one group of each scattering center of parametric description, and these attributes all are the important informations that concerns target; Compare with the point scattering model, the attribute scattering center model has comprised the abundanter feature that can be used for target classification identification.

The feature extraction of target scattering center is a process of estimating each scattering center parameter from the target echo data in essence.Because attribute scattering center model complex structure and parameter dimension are higher, increased the complicacy of model parameter estimation.Existing method obtains the lower target scattering district of exponent number or isolated scattering center by the radar image that obtains as the basis take the point scattering model is carried out image segmentation, utilizes the attribute scattering center parameter of approximate maximum likelihood method estimating target.At first because existing method utilization is extracted the attribute scattering center according to the radar image that the point scattering model obtains, so there is the model mismatch problem; Secondly since these class methods take image segmentation as the basis, so these class methods require picture quality higher, when some parts scattering strength of target is weak, be difficult to correct the detection by image partition method in addition, this just causes some key characters of target easily to be lost.Optimization problem owing to these class methods is non-protruding problem in addition, and has a lot of local minimal solutions, thus the problem that exists parameter initialization, model order selection and scattering center structured sort to differentiate, so that the final argument estimated accuracy is lower.

Summary of the invention

The object of the invention is to propose a kind of method of the radar target attribute scattering center feature extraction based on Its Sparse Decomposition, the model mismatch, the feature that exist in the existing method are easily lost and the low problem of Parameter Estimation Precision to solve.

The present invention is achieved in that

One. technical thought

In the radar return, target scattering field overwhelming majority energy illustrates that only by the contribution of a small amount of strong scattering center radar return has very strong sparse property at the parameter space of attribute scattering center.Consider that attribute scattering center parameter space dimension is higher, the redundant dictionary dimension that causes constructing is far longer than our accessible dimension, method of the present invention is based on sparse resolution theory, and utilize coordinate samsara decline Techniques For Reducing problem dimension and make up the super-resolution dictionary, extract attribute scattering center feature by finding the solution 0 norm optimization problem; Set up the scattering center strength threshold and in radar image, carry out the strong scattering Spot detection, determine the value set of scattering center parameter in conjunction with prior imformation; According to the attribute scattering center model, utilize coordinate samsara descent method technique construction super-resolution dictionary, obtain the parameter estimation set of attribute scattering center and target and vitals geometries characteristic thereof.

Two. technical scheme

Performing step of the present invention comprises as follows:

1) sets scattering center strength threshold ξ according to noise in the radar image, intensity in the radar image is defined as the strong scattering center greater than the scattering center of ξ, according to the strong scattering centre coordinate (x that detects, y) determine coordinate parameters x, the span of y, determine scattering center length L span by prior imformation, set distributed scattering center position angle

Final definite scattering center parameter Set

2) according to described parameter sets

Make up dictionary

2a) with dictionary

Parameter sets

Discretize, the interval that is about to the adjacent coordinates parameter x is made as a Range resolution element length ρ _r, the interval of adjacent coordinates parameter y is made as an azimuth discrimination element length ρ _a, the interval of adjacent scattering center length parameter L is made as ρ _a

2b) according to the attribute scattering center model, produce the atom d of corresponding different parameters _i(f, φ)

$d_i(f,\mathrm{\&phi;})=\exp \left(\frac{-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="DEST\_PATH\_HDA00002876017000012.png"\; state="\{\{state\}\}">j</figure-callout>}4\mathrm{\&pi;f}}{c}(x_i\cos \mathrm{\&phi;}+y_i\sin \mathrm{\&phi;})\right)\&CenterDot;$

$\sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_i\sin (\mathrm{\&phi;}-\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_i})\right)---<1>$

i＝1，…N ₀

Wherein i represents atom sequence number, N ₀Expression is dictionary when (x, y, L) according to a preliminary estimate

The atom number, exp () is natural exponential function, sinc () is Sinc function,

Be set

I group parameter after the discretize, f is the radar emission signal frequency, and φ is the radar beam position angle, and c is the light velocity;

To not homoatomic d _i(f, φ) column vector, and former subvector carried out energy normalized, make up dictionary For:

$D_0(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_0}]$

${\hat{d}}_i=\frac{\mathrm{vec}\left(d_i(f,\mathrm{\&phi;})\right)}{{\left|\right|\mathrm{vec}\left(d_i(f,\mathrm{\&phi;})\right)\left|\right|}_2}---<2>$

Wherein vec () expression column vector operation, || || ₂Be 2 norm operators;

3) utilize orthogonal matching pursuit OMP method to find the solution suc as formula＜3〉0 norm optimization problem, by σ ₁Upgrade the scattering center parameter sets

According to a preliminary estimate set for scattering center parameter (x, y, L);

${\mathrm{\&sigma;}}_1=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_0(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<3>$

Wherein, σ is scattering coefficient vector to be optimized, σ ₁Be the scattering coefficient vector of optimizing, s is the vectorization of frequency domain observation signal matrix column, || || ₀Be 0 norm operator, ε is the energy error constraint factor, and the energy Ratios that accounts for the view picture radar image according to the object support district is determined;

4) according to described parameter sets

Make up dictionary

4a) determine scattering center length L span according to prior imformation, the interval of adjacent scattering center length parameter L is made as ρ _a, obtain dictionary The discrete value of scattering center length parameter L; Determine distributed scattering center position angle according to the orientation angular domain of radar return data recording

Span is with adjacent distributions formula scattering center position angle parameter

The interval be made as

Obtain dictionary

Distributed scattering center position angle parameter

Discrete value; The scattering center coordinate parameters

4b) according to scattering center length parameter L and the distributed scattering center position angle of discretize

By formula＜1〉produce former subvector, and atom is carried out energy normalized, make up dictionary

For:

$D_1(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_1}]---<4>$

N wherein ₁The expression estimated parameter

The time dictionary

The atom number;

5) utilize orthogonal matching pursuit OMP method to find the solution suc as formula＜5〉0 norm optimization problem, by σ ₂Upgrade the scattering center parameter sets

Be parameter

Valuation set;

${\mathrm{\&sigma;}}_2=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_1(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<5>$

σ wherein ₂Be the scattering coefficient vector of optimizing;

6) according to described parameter sets

Make up the super-resolution dictionary

6a) with In coordinate parameters x centered by, length is ρ _rNeighborhood in value, the interval of adjacent parameter x is made as ρ _r/ N _s, obtain dictionary

The discrete value of coordinate parameters x, N _sBe super-resolution multiple, General N _s=2,4,8 ...; With

In y centered by, length is ρ _aNeighborhood in value, the interval of adjacent parameter y is made as ρ _a/ N _s, obtain dictionary

The discrete value of coordinate parameters y; With

In L centered by, length is ρ _aNeighborhood in value, the interval of adjacent parameter L is made as ρ _a/ N _s, obtain dictionary

The discrete value of scattering center length parameter L; Distributed scattering center position angle parameter

6b) according to the dictionary parameter x of discretize, y, L is by formula＜1〉produce former subvector, and atom is carried out energy normalized, make up the super-resolution dictionary

$D_2(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_2}]---<6>$

Wherein, N ₂Expression super-resolution dictionary

The atom number;

7) utilize orthogonal matching pursuit OMP method to find the solution suc as formula＜7〉0 norm optimization problem, by σ ₃Upgrade the scattering center parameter sets The super-resolution that obtains (x, y, L) is estimated set

With target and vitals geometries characteristic thereof;

${\mathrm{\&sigma;}}_3=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_2(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<7>$

σ wherein ₃Be the scattering coefficient vector of optimizing.

The present invention compared with prior art has the following advantages:

(1) there is the model mismatch problem in the existing method of extracting attribute scattering center feature, and because image segmentation can cause some important scattering centers of target to be easy to lose.The present invention propose based on the radar target attribute scattering center feature extracting method of Its Sparse Decomposition from the frequency domain observation data, obtain the rarefaction representation of frequency domain observation data by finding the solution 0 norm optimization problem, can effectively extract target scattering center.

(2) existing method is carried out parameter initialization and model order and is selected based on the result that radar image is cut apart, and estimates the parameter of the attribute scattering center in the radar image subregion by approximate maximum likelihood method, and the parameters precision that these class methods are estimated is lower.The inventive method is carried out Its Sparse Decomposition by utilizing coordinate samsara decline technique construction super-resolution dictionary to the frequency domain observation data, and the super-resolution that obtains radar target attribute scattering center parameter is estimated.

(3) the present invention can effectively extract target scattering center owing to the inventive method, and obtain the super-resolution estimation of scattering center parameter, so according to the scattering center parameter sets of extracting, can obtain the precise geometrical size characteristic of target and vitals thereof.

Description of drawings

Fig. 1 is process flow diagram of the present invention;

To be attribute scattering center model medium frequency dependent factor α=1 change waveform with the frequency of distance numeric field data of frequency dependent factor-alpha=0 o'clock to Fig. 2;

Fig. 3 is orientation dependent factor γ=10 in the attribute scattering center model ^-11Change waveform with the orientation frequency domain data of orientation dependent factor γ=0 o'clock;

Fig. 4 is the original radar image of radar target T72 tank;

Fig. 5 is by the radar image of the inventive method to the radar target T72 tank of Fig. 4 reconstruct;

Fig. 6 is original radar target D7 forklift radar image;

Fig. 7 is by the radar target D7 forklift radar image of the inventive method to Fig. 6 reconstruct.

Embodiment

One, know-why

The tradition radar image obtains as the basis take the point scattering model, and this model only comprises the target scattering dot position information, but only utilize the recognition feature of the positional information structure of target scattering point can not complete sign radar image in the essential attribute of target.In optical zone, the high-frequency electromagnetic scattering response of expansion target can be with the scatterer of one group of independent distribution, or the electromagnetic scattering response sum approximate representation of title scattering center.The attribute scattering center model is with position, shape, direction and the amplitude etc. of one group of each scattering center of parametric description, and these attributes all are the important informations that concerns target; Compare with the point scattering model, the attribute scattering center model has comprised the abundanter feature that can be used for target classification identification.

According to the attribute scattering center model as can be known, i scattering center frequency-orientation two dimension echoed signal is in the target:

$E_i(f,\mathrm{\&phi;};{\mathrm{\&theta;}}_i)=A_i\&CenterDot;{\left(j\frac{f}{f_c}\right)}^{{\mathrm{\&alpha;}}_i}\exp \left(\frac{-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="DEST\_PATH\_HDA00002876017000012.png"\; state="\{\{state\}\}">j</figure-callout>}4\mathrm{\&pi;f}}{c}(x_i\cos \mathrm{\&phi;}+y_i\sin \mathrm{\&phi;})\right)\&CenterDot;---<8>$

$\sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_i\sin (\mathrm{\&phi;}-\stackrel{\&OverBar;}{{\mathrm{\&theta;}}_i})\right)\exp (-2\mathrm{\&pi;f}{\mathrm{\&gamma;}}_i\sin \mathrm{\&phi;})$

Wherein, i represents the scattering center sequence number, and f is the radar emission signal frequency, and φ is the radar bearing angle, and exp () is natural exponential function, and sin c () is Sinc function, and c is the light velocity, θ _iThe parameter vector that represents i scattering center

Ai is the scattering strength of scattering center, x _iBe distance dimension coordinate, y _iBe azimuth dimension coordinate, L _iBe the length of distributed scattering center azimuth dimension,

Be the position angle of distributed scattering center, α _iBe the frequency dependent factor, general α _i∈ 1 ,-0.5,0,0.5,1}, γ _iOrientation dependent factor for local formula scattering center.

By the echoed signal sum of each scattering center, can consist of target frequency-orientation two dimension echoed signal:

$E(f,\mathrm{\&phi;};\mathrm{\&theta;})=\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{E}_i(f,\mathrm{\&phi;};{\mathrm{\&theta;}}_i),$ ${\mathrm{\&theta;}}^T=[{\mathrm{\&theta;}}_1^T,...,{\mathrm{\&theta;}}_i,...,{\mathrm{\&theta;}}_M^T]---<9>$

Wherein i represents scattering center sequence number, E _i(f, φ; θ _i) be the echoed signal of i scattering center, M is the scattering center number, θ represents M scattering center parameter matrix, () ^TThe expression matrix transpose operation;

With formula＜9〉target echo signal express with matrix form, its expression formula is:

s=D(θ)σ+n <10>

Wherein s is target echo signal E (f, φ; Column vector θ), D (θ) is dictionary corresponding to scattering center parameter matrix θ, and σ is the scattering coefficient vector, and n represents white Gaussian noise.

In radar return, because most energy of target scattering field are only by the contribution of a small amount of strong scattering center, therefore the explanation radar return has very strong sparse property at the parameter space of attribute scattering center.According to the sparse property of radar return at the parameter space of attribute scattering center, can obtain the rarefaction representation of observation data s by finding the solution 0 norm optimization problem, and scattering center parameter estimation set, can estimating target and the geometries characteristic of vitals by the scattering center parameter sets.

Because attribute scattering center parameter space dimension is higher, the redundant dictionary dimension that causes constructing is far longer than need dimension to be processed, therefore can be by the impact on echoed signal of the frequency dependent factor-alpha in the analytic attribute scattering center model, orientation dependent factor γ, the attribute scattering center model is simplified, reduced the parameter space dimension.

Centre frequency f when radar _c=9.6GHz, bandwidth B=591MHz, other scattering center parameter is 0 o'clock, only change frequency dependent factor-alpha or orientation dependent factor γ, and frequency dependent factor-alpha and orientation dependent factor γ has following impact to the frequency domain echo data:

A) because the radar relative bandwidth is less, the frequency dependent factor-alpha makes the scattering strength of scattering center in the frequency of distance dimension subtle change can occur, as shown in Figure 2, Fig. 2 (a) medium frequency dependent factor α=1 wherein, Fig. 2 (b) medium frequency dependent factor α=0.

B) because radar bearing angle φ variation range is less, the variation of local formula scattering center orientation dependent factor γ can make the scattering strength of local formula scattering center slightly change on the orientation frequency, as shown in Figure 3, orientation dependent factor γ=10 among Fig. 3 (a) wherein ^-11, orientation dependent factor γ among Fig. 3 (b)=0.

By above analysis as can be known, frequency dependent factor-alpha and orientation dependent factor γ are very little to target frequency domain echo data influence, so estimated parameter The time can ignore frequency dependent factor-alpha and orientation dependent factor γ, namely think frequency dependent factor-alpha=0, orientation dependent factor γ=0, then primitive attribute scattering center model formula＜8〉can be reduced to:

${\hat{E}}_i(f,\mathrm{\&phi;};{\mathrm{\&theta;}}_i)=A_i\&CenterDot;\exp \left(\frac{-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="DEST\_PATH\_HDA00002876017000012.png"\; state="\{\{state\}\}">j</figure-callout>}4\mathrm{\&pi;f}}{c}(x_i\cos \mathrm{\&phi;}+y_i\sin \mathrm{\&phi;})\right)\&CenterDot;$ $<11>$

$\sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_i\sin (\mathrm{\&phi;}-\stackrel{\&OverBar;}{{\mathrm{\&theta;}}_i})\right)$

According to the attribute scattering center model after simplifying, based on Its Sparse Decomposition, utilize coordinate samsara decline technology, the super-resolution that can obtain the target scattering center parameter estimates, can estimating target and the geometries characteristic of vitals by the scattering center parameter sets.

Two, performing step

With reference to Fig. 1, performing step of the present invention is as follows:

Step 1 is set up scattering center strength threshold ξ and is carried out the strong scattering Spot detection, determines scattering center parameter value scope.

1a) radar imagery:

By formula＜11〉as can be known, radar echo signal is uniform sampling under frequency-orientation polar coordinate space, and radar imagery resamples echoed signal or interpolation, obtains at cartesian coordinate system (f _x, f _y) the echoed signal E (f of lower uniform sampling _x, f _y), f wherein _xBe frequency of distance, f _yBe the orientation frequency;

f _x＝fcos(φ)，f _y＝fsin(φ) <12>

Wherein, φ is the radar bearing angle;

To echoed signal E (f _x, f _y) do two-dimentional inverse Fourier transform, obtain the radar image of target;

1b) strong scattering Spot detection, determine scattering center parameter value scope:

Set scattering center strength threshold ξ according to noise in the radar image, intensity in the radar image is defined as the strong scattering center greater than the scattering center of ξ, according to the strong scattering centre coordinate (x that detects, y) determine coordinate parameters x, the span of y, determine scattering center length L span by prior imformation, set distributed scattering center position angle Final definite scattering center parameter

Set

For example, when radar image data for open MSTAR measured data in the position angle be that 80.774185 ° of angles of pitch are when being 15 ° T72 tank data, set scattering center strength threshold ξ=0.28 according to noise in the radar image, the span of the scattering center range coordinate parameter x of determining is [11.1675,14.467] rice, and the span of azimuthal coordinates parameter y is [13.40625,4.875] rice, scattering center length L span is [0,4.0625] rice, distributed scattering center position angle

Step 2 is according to described parameter sets

Make up dictionary

2a) with dictionary

Parameter sets

Discretize, the interval that is about to the adjacent coordinates parameter x is made as a Range resolution element length ρ _r, the interval of adjacent coordinates parameter y is made as an azimuth discrimination element length ρ _a, the interval of adjacent scattering center length parameter L is made as ρ _a

For example, when radar image data for open MSTAR measured data in the position angle be that 80.774185 ° of angles of pitch are when being 15 ° T72 tank data, set scattering center strength threshold ξ=0.28 according to noise in the radar image, the span of the scattering center range coordinate parameter x of determining is [11.1675,14.467] rice, the adjacent coordinates parameter x is spaced apart 0.2538 meter, the span of azimuthal coordinates parameter y is [13.40625,4.875] rice, the interval of adjacent coordinates parameter y is made as 0.203125 meter, scattering center length L span is [0,4.0625] rice, the interval of adjacent scattering center length parameter L is made as 0.203125 meter, distributed scattering center position angle

2b) according to the attribute scattering center model, produce the atom d of corresponding different parameters _i(f, φ):

$d_i(f,\mathrm{\&phi;})=\exp \left(\frac{-\mathrm{<figure-callout\; id="4"\; label="j"\; filenames="DEST\_PATH\_HDA00002876017000012.png"\; state="\{\{state\}\}">j</figure-callout>}4\mathrm{\&pi;f}}{c}(x_i\cos \mathrm{\&phi;}+y_i\sin \mathrm{\&phi;})\right)\&CenterDot;$

$\sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_i\sin (\mathrm{\&phi;}-\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_i})\right)---<13>$

i＝1，…N ₀

Wherein, f is the radar emission signal frequency, and φ is the radar bearing angle, and exp () is natural exponential function, and sin c () is Sinc function, and c is the light velocity, and i represents atom sequence number, N ₀Expression is dictionary when (x, y, L) according to a preliminary estimate

The atom number, Be set

I group parameter after the discretize.

2c) incite somebody to action not homoatomic d _i(f, φ) column vector, and former subvector carried out energy normalized, make up dictionary

$D_0(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_0}]$

${\hat{d}}_i=\frac{\mathrm{vec}\left(d_i(f,\mathrm{\&phi;})\right)}{{\left|\right|\mathrm{vec}\left(d_i(f,\mathrm{\&phi;})\right)\left|\right|}_2}$ <14>

i=1，…N ₀

Wherein, i represents atom sequence number, N ₀Expression is dictionary when (x, y, L) according to a preliminary estimate

The atom number, the operation of vec () expression column vector, || || ₂Be 2 norm operators.

Step 3 utilizes orthogonal matching pursuit OMP to find the solution suc as formula＜15〉0 norm optimization problem:

${\mathrm{\&sigma;}}_1=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_0(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<15>$

Wherein σ is scattering coefficient vector to be optimized, σ ₁Be the scattering coefficient vector of optimizing, s is the vectorization of frequency domain observation signal matrix column, || || ₀Be 0 norm operator, ε is the energy error constraint factor, and it is determined according to the energy Ratios that the object support district accounts for the view picture radar image.

The solution procedure of this step is as follows:

3a) input dictionary

3b) initialization is about to signal margin r and is initialized as frequency domain observation signal matrix column vector s, and scattering coefficient vector σ is initialized as 0, and atom index vector a is initialized as sky, establishes primary iteration number of times k=1, and the beginning iteration;

3c) the related coefficient of Dictionary of Computing and signal margin r vector C

$C=D_0{(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)}^H\&CenterDot;r---<16>$

Wherein () ^HThe expression conjugate transpose, the sequence number of greatest member is a among the related coefficient vector C _k, can get atom index vector a and be:

a=[a ₁，…，a _k] <17>

3d) utilize least square method calculation method for scattering coefficient vector σ

Wherein

The expression pseudoinverse, D ₀(:, a) be dictionary D ₀Middle row number are a _iThe matrix i=1 that consists of of k column vector ..., k, k are the current iteration number of times;

Upgrade surplus r:

r＝s-D ₀(：，a)·σ(a) <19>

Wherein σ (a) is a for sequence number among the scattering coefficient vector σ _iThe column vector i=1 that consists of of k element ..., k;

3e) calculate reconstruct energy Ratios η _k

${\mathrm{\&eta;}}_k=\frac{\mathrm{\&Sigma;}{\left|\right|s_k\left|\right|}_2^2}{\mathrm{\&Sigma;}{\left|\right|s\left|\right|}_2^2}---<20>$

s _k=D ₀(：，a)·σ(a)

S wherein _kBe reconstruction signal, Represent 2 norms square;

If 3f) η _k-η _K-1≤ δ stops iteration, σ ₁=σ, wherein δ is the thresholding of the difference of adjacent iteration energy Ratios, gets δ=0.001; Otherwise k=k+1 also goes to step 3c).

Step 4 is by the scattering coefficient vector σ that optimizes ₁Upgrade the scattering center parameter sets

According to a preliminary estimate set for scattering center parameter (x, y, L).

Step 5 is according to described parameter sets

Make up dictionary

5a) determine scattering center length L span according to prior imformation, the interval of adjacent scattering center length parameter L is made as ρ _a, obtain dictionary The discrete value of scattering center length parameter L; Determine distributed scattering center position angle according to the orientation angular domain of radar return data recording

Span is with adjacent distributions formula scattering center position angle parameter

The interval be made as

Obtain dictionary

Distributed scattering center position angle parameter Discrete value; The scattering center coordinate parameters

For example, when radar image data for open MSTAR measured data in the position angle be that 80.774185 ° of angles of pitch are when being 15 ° T72 tank data, scattering center length L span is [0,4.0625] rice, the interval of adjacent scattering center length parameter L is made as 0.203125 meter, distributed scattering center position angle

Span be [3 °, 3 °], with adjacent distributions formula scattering center position angle parameter

The interval be made as 0.25 °.

5b) according to scattering center length parameter L and the distributed scattering center position angle of discretize

By formula＜13〉produce former subvector, and former subvector is carried out energy normalized, make up dictionary

For:

$D_1(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_1}]---<21>$

Wherein, i represents the atom sequence number, i=1 ... N ₁, N ₁The expression estimated parameter

The time dictionary

The atom number.

Step 6 utilizes orthogonal matching pursuit OMP to find the solution suc as formula＜22〉0 norm optimization problem:

${\mathrm{\&sigma;}}_2=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_1(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<22>$

σ wherein ₂Be the scattering coefficient vector of optimizing, its solution procedure is as follows:

6a) input dictionary

6b) initialization is about to signal margin r and is initialized as frequency domain observation signal matrix column vector s, and scattering coefficient vector σ is initialized as 0, and atom index vector a is initialized as sky, establishes primary iteration number of times k=1, and the beginning iteration;

6c) the related coefficient of Dictionary of Computing and signal margin r vector C

$C=D_1{(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)}^H\&CenterDot;r---<23>$

Wherein () ^HThe expression conjugate transpose, the sequence number of greatest member is a among the related coefficient vector C _k, can get atom index vector a and be:

a=[a ₁，…，a _k] <24>

6d) utilize least square method calculation method for scattering coefficient vector σ

Wherein

The expression pseudoinverse, D ₁(:, a) be dictionary D ₁Middle row number are a _iThe matrix i=1 that consists of of k column vector ..., k, k are the current iteration number of times;

Upgrade surplus r:

r=s-D ₁(：，a)·σ(a) <26>

Wherein σ (a) is a for sequence number among the scattering coefficient vector σ _iThe column vector i=1 that consists of of k element ..., k;

6e) calculate reconstruct energy Ratios η _k

${\mathrm{\&eta;}}_k=\frac{\mathrm{\&Sigma;}{\left|\right|s_k\left|\right|}_2^2}{\mathrm{\&Sigma;}{\left|\right|s\left|\right|}_2^2}---<27>$

s _k=D ₁(：，a)·σ(a)

S wherein _kBe reconstruction signal,

Represent 2 norms square;

If 6f) η _k-η _K-1≤ δ stops iteration, σ ₂=σ, wherein δ is the thresholding of the difference of adjacent iteration energy Ratios, gets δ=0.001; Otherwise k=k+1 also goes to step 6c).

Step 7 is by the scattering coefficient vector σ that optimizes ₂Upgrade the scattering center parameter sets

Be parameter

Valuation set.

Step 8 is according to described parameter sets

Make up the super-resolution dictionary

8a) determine dictionary

Apart from the discrete value of dimension coordinate parameter x: with parameter sets

In apart from centered by the dimension coordinate parameter x, length is ρ _rNeighborhood in value, the interval of adjacent parameter x is made as ρ _r/ N _s, obtain dictionary

The discrete value apart from the dimension coordinate parameter x, N wherein _sBe super-resolution multiple, General N _s=2,4,8 ...;

8b) determine dictionary

The discrete value of azimuth dimension coordinate parameters y:

With parameter sets

In azimuth dimension coordinate parameters y centered by, length is ρ _aNeighborhood in value, the interval of adjacent parameter y is made as ρ _a/ N _s, obtain dictionary

The discrete value of azimuth dimension coordinate parameters y;

8c) determine dictionary

The discrete value of scattering center length parameter L:

With parameter sets In scattering center length parameter L centered by, length is ρ _aNeighborhood in value, the interval of adjacent parameter L is made as ρ _a/ N _s, obtain dictionary

The discrete value of scattering center length parameter L;

8d) determine dictionary

Distributed scattering center position angle parameter

Discrete value:

With parameter sets

In distributed scattering center position angle parameter

Be dictionary

Distributed scattering center position angle parameter

8e) according to above-mentioned steps determine apart from the dimension coordinate parameter x, azimuth dimension coordinate parameters y, scattering center length parameter L, distributed scattering center position angle parameter

Discrete value is by formula＜13〉produce the former subvector corresponding with the dictionary parameter combinations of discretize, and atom is carried out energy normalized, make up the super-resolution dictionary

For:

$D_2(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_2}]---<28>$

Wherein, i represents atom sequence number, i=1...N ₂, N ₂Expression super-resolution dictionary

The atom number.

Step 9 utilizes orthogonal matching pursuit OMP method to find the solution suc as formula＜29〉0 norm optimization problem:

${\mathrm{\&sigma;}}_3=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_2(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<29>$

σ wherein ₃Be the scattering coefficient vector of optimizing, its solution procedure is as follows:

9a) input dictionary

9b) initialization is about to signal margin r and is initialized as frequency domain observation signal matrix column vector s, and scattering coefficient vector σ is initialized as 0, and atom index vector a is initialized as sky, establishes primary iteration number of times k=1, and the beginning iteration;

9c) the related coefficient of Dictionary of Computing and signal margin r vector C

$C=D_2{(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)}^H\&CenterDot;r---<30>$

Wherein () ^HThe expression conjugate transpose, the sequence number of greatest member is a among the related coefficient vector C _k, obtain atom index vector a and be:

a=[a ₁，…，a _k] <31>

9d) utilize least square method calculation method for scattering coefficient vector σ

Wherein

The expression pseudoinverse, D ₂(:, a) be dictionary D ₂Middle row number are a _iThe matrix i=1 that consists of of k column vector ..., k, k are the current iteration number of times;

Upgrade surplus r:

r=s-D ₂(：，a)·σ(a) <33>

Wherein σ (a) is a for sequence number among the scattering coefficient vector σ _iThe column vector i=1 that consists of of k element ..., k;

9e) calculate reconstruct energy Ratios η _k:

${\mathrm{\&eta;}}_k=\frac{\mathrm{\&Sigma;}{\left|\right|s_k\left|\right|}_2^2}{\mathrm{\&Sigma;}{\left|\right|s\left|\right|}_2^2}---<34>$

s _k=D ₂(：，a)·σ(a)

S wherein _kBe reconstruction signal,

Represent 2 norms square;

If 9f) η _k-η _K-1≤ δ stops iteration, and σ 3=σ wherein δ is the thresholding of the difference of adjacent iteration energy Ratios, gets δ=0.001; Otherwise k=k+1 also goes to step 9c).

Step 10 is by the scattering coefficient vector σ that optimizes ₃Upgrade the scattering center parameter sets

The super-resolution that obtains (x, y, L) is estimated set

According to the scattering center parameter sets

Estimating target and vitals geometries characteristic thereof.

For example, when radar image data for open MSTAR measured data in the position angle be that 80.774185 ° of angles of pitch are when being 15 ° T72 tank data, according to scattering center and the parameter sets thereof of final extraction

The physical dimension of estimating the T72 tank is: T72 tank gun tube length degree is 6.4 meters, and the tank body length is 6.8 meters, and the total length of T72 tank is 9.4 meters, and the width valuation of T72 tank is 3.8 meters.

Effect of the present invention further specifies by following experiment to measured data:

1) experiment scene:

Synthetic-aperture radar SAR data and the position angle of testing used measured data and be disclosed MSTAR data centralization position angle and be 80.774185 ° of angles of pitch and be 15 ° T72 tank are that 0.307442 ° of angle of pitch is the SAR data of 17 ° D7 forklift, the centre frequency f of radar _c=9.6GHz, bandwidth B=591MHz.T72 tank true geometric is of a size of: the long 6.41m of car body, overall width 3.52m, the long 6.155m of gun barrel, big gun be gun barrel extension elongation 3.035m forward the time.D7 forklift true geometric is of a size of: overall width 2.56m, vehicle commander 4.2m, overall height 3.294m, track shoe width 0.56m, track gage 1.981m, ground connection track length 2.72m.2) experiment content:

Be that 80.774185 ° of angles of pitch are 15 ° T72 tank MSTAR data for the position angle 2a), utilize coordinate samsara descent method to make up the super-resolution dictionary, obtain the set of scattering center parameter estimation by finding the solution 0 norm optimization problem.Fig. 4 is original T72 tank SAR image, according to the T72 tank image of the scattering center of extracting and parameter reconstruct thereof as shown in Figure 5, and by Fig. 4 and Fig. 5 accurate reconstruct target image of the present invention as can be known.

Be that 0.307442 ° of angle of pitch is 17 ° D7 forklift MSTAR data for the position angle 2b), utilize coordinate samsara descent method to make up the super-resolution dictionary, obtain the set of scattering center parameter estimation by finding the solution 0 norm optimization problem.Fig. 6 is original D7 forklift SAR image, according to the T72 tank image of the scattering center of extracting and parameter reconstruct thereof as shown in Figure 7, and by Fig. 6 and Fig. 7 accurate reconstruct target image of the present invention as can be known.

3) interpretation:

Table 1 the inventive method is processed T72 tank data convergence process

	Step 3	Step 6	Step 9
				The reconstruct energy Ratios	79.8％	83.7％	86.5％
Dictionary atom number	9030	63000	47000
				The scattering center number	126	94	92

Table 2 the inventive method is processed D7 forklift data convergence process

	Step 3	Step 6	Step 9
				The reconstruct energy Ratios	84％	86.7％	88.7％
Dictionary atom number	4800	31125	29925
				The scattering center number	83	57	57

Table 1 and table 2 have provided respectively the convergence situation that method of the present invention is processed reconstruct energy Ratios, dictionary atom number and scattering center number in T72 tank and the D7 forklift data procedures.Because step 3 supposition

And only parameter (x, y, L) is carried out according to a preliminary estimate, so the reconstruct energy of step 3 is lower; When step 6 is considered distributed scattering center position angle on the basis of step 3

The time, the reconstruct energy Ratios is improved, and the scattering center number of extraction reduces; The parameter resolution of dictionary increases in the step 9, and the reconstruct energy Ratios is improved, and the scattering center number also further reduces, and dictionary atom number is reduced, this be since step 3 to having utilized coordinate samsara decline technology between the step 9.The data convergence process shows that the inventive method can effectively extract scattering center in table 1, the table 2.

The physical dimension that can estimate T72 tank and D7 forklift according to scattering center and the parameter thereof of final extraction.

Table 3 is used for estimating the scattering center parameter of T72 tank gun tube length degree

Table 3 shows, estimates that according to coordinate and the scattering center length of scattering center tank gun tube length degree is 6.4 meters.

Table 4 is used for estimating the scattering center parameter of T72 tank body length

Table 4 shows, estimates that according to coordinate parameters and the scattering center length of scattering center the tank body length is 6.8 meters.

The total length valuation that can be obtained the T72 tank by the object support district is 9.4 meters; Be half of T72 tank width according to the scattering center of T72 tank coboundary to the distance of gun barrel scattering center, the width valuation that obtains the T72 tank is 3.8 meters.

Table 5 is used for estimating the scattering center parameter of D7 forklift blade length

Table 5 shows, estimates that according to coordinate parameters and the scattering center length of scattering center D7 forklift perching knife length is 3 meters.

Table 6 is used for estimating the scattering center parameter of D7 forklift width

Table 6 shows, estimates that according to coordinate parameters and the scattering center length of scattering center D7 forklift width is 2.6 meters.

Table 7 is used for estimating the scattering center parameter of D7 forklift crawler width

Table 7 shows, estimates that according to coordinate parameters and the scattering center length of scattering center D7 forklift crawler width is 0.6 meter.

Can estimate that by the crawler belt scattering center of extracting the ground connection track length of D7 forklift is 2.6 meters; Obtaining D7 forklift vehicle commander valuation by the object support district is 4.31 meters.

True geometric size in conjunction with T72 tank and D7 forklift, the physical dimension error of the target of the inventive method estimation and vitals thereof is in 6% as can be known, and experimental result explanation the inventive method can accurately be extracted the physical dimension of objective attribute target attribute scattering center feature and accurate estimating target and vitals thereof effectively.

Claims (4)

1. the radar target attribute scattering center feature extracting method based on Its Sparse Decomposition comprises the steps:

1) sets scattering center strength threshold ξ according to noise in the radar image, intensity in the radar image is defined as the strong scattering center greater than the scattering center of ξ, according to the strong scattering centre coordinate (x that detects, y) determine coordinate parameters x, the span of y, determine scattering center length L span by prior imformation, set distributed scattering center position angle Final definite scattering center parameter

Set

2) according to described parameter sets Make up dictionary

2a) with dictionary

Parameter sets

Discretize, the interval that is about to the adjacent coordinates parameter x is made as a Range resolution element length ρ _r, the interval of adjacent coordinates parameter y is made as an azimuth discrimination element length ρ _a, the interval of adjacent scattering center length parameter L is made as ρ _a

2b) according to the attribute scattering center model, produce the atom d of corresponding different parameters _i(f, φ)

$d_i(f,\mathrm{\&phi;})=\exp \left(\frac{-j4\mathrm{\&pi;f}}{c}(x_i\cos \mathrm{\&phi;}+y_i\sin \mathrm{\&phi;})\right)\&CenterDot;$

$\sin c\left(\frac{2\mathrm{\&pi;f}}{c}{L}_i\sin (\mathrm{\&phi;}-\stackrel{\&OverBar;}{{\mathrm{\&phi;}}_i})\right)---<1>$

i＝1,...N ₀

Wherein i represents atom sequence number, N ₀Expression is dictionary when (x, y, L) according to a preliminary estimate

The atom number, exp () is natural exponential function, sinc () is Sinc function,

Be set I group parameter after the discretize, f is the radar emission signal frequency, and φ is the radar beam position angle, and c is the light velocity;

To not homoatomic d _i(f, φ) column vector, and former subvector carried out energy normalized, make up dictionary

For:

$D_0(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_0}]$

${\hat{d}}_i=\frac{\mathrm{vec}\left(d_i(f,\mathrm{\&phi;})\right)}{{\left|\right|\mathrm{vec}\left(d_i(f,\mathrm{\&phi;})\right)\left|\right|}_2}---<2>$

Wherein vec () expression column vector operation, || || ₂Be 2 norm operators;

3) utilize orthogonal matching pursuit OMP method to find the solution suc as formula＜3〉0 norm optimization problem, by σ ₁Upgrade the scattering center parameter sets

According to a preliminary estimate set for scattering center parameter (x, y, L);

${\mathrm{\&sigma;}}_1=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_0(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<3>$

Wherein, σ is scattering coefficient vector to be optimized, σ ₁Be the scattering coefficient vector of optimizing, s is the vectorization of frequency domain observation signal matrix column, || || ₀Be 0 norm operator, ε is the energy error constraint factor, and the energy Ratios that accounts for the view picture radar image according to the object support district is determined;

4) according to described parameter sets

Make up dictionary

4a) determine scattering center length L span according to prior imformation, the interval of adjacent scattering center length parameter L is made as ρ _a, obtain dictionary

The discrete value of scattering center length parameter L; Determine distributed scattering center position angle according to the orientation angular domain of radar return data recording

Span is with adjacent distributions formula scattering center position angle parameter

The interval be made as Obtain dictionary Distributed scattering center position angle parameter

Discrete value; The scattering center coordinate parameters

4b) according to scattering center length parameter L and the distributed scattering center position angle of discretize

By formula＜1〉produce former subvector, and atom is carried out energy normalized, make up dictionary

For:

$D_1(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_1}]---<4>$

N wherein ₁The expression estimated parameter

The time dictionary

The atom number;

5) utilize orthogonal matching pursuit OMP method to find the solution suc as formula＜5〉0 norm optimization problem, by σ ₂Upgrade the scattering center parameter sets

Be parameter

Valuation set;

${\mathrm{\&sigma;}}_2=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_1(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<5>$

σ wherein ₂Be the scattering coefficient vector of optimizing;

6) according to described parameter sets

Make up the super-resolution dictionary

6a) with

In coordinate parameters x centered by, length is ρ _rNeighborhood in value, the interval of adjacent parameter x is made as ρ _r/ N _s, obtain dictionary

The discrete value of coordinate parameters x, N _sBe super-resolution multiple, General N _s=2,4,8 ...; With

In y centered by, length is ρ _aNeighborhood in value, the interval of adjacent parameter y is made as ρ _a/ N _s, obtain dictionary

The discrete value of coordinate parameters y; With

In L centered by, length is ρ _aNeighborhood in value, the interval of adjacent parameter L is made as ρ _a/ N _s, obtain dictionary

The discrete value of scattering center length parameter L; Distributed scattering center position angle parameter

6b) according to the dictionary parameter x of discretize, y, L is by formula＜1〉produce former subvector, and atom is carried out energy normalized, make up the super-resolution dictionary

$D_2(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)=[{\hat{d}}_1,...,{\hat{d}}_i,...,{\hat{d}}_{N_2}]---<6>$

Wherein, N ₂Expression super-resolution dictionary The atom number;

7) utilize orthogonal matching pursuit OMP method to find the solution suc as formula＜7〉0 norm optimization problem, by σ ₃Upgrade the scattering center parameter sets

The super-resolution that obtains (x, y, L) is estimated set

With target and vitals geometries characteristic thereof;

${\mathrm{\&sigma;}}_3=\arg \underset{\mathrm{\&sigma;}}{\min }{\left|\right|\mathrm{\&sigma;}\left|\right|}_0,$ $s.t.{\left|\right|s-D_2(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)\&CenterDot;\mathrm{\&sigma;}\left|\right|}_2\&le;\mathrm{\&epsiv;}---<7>$

σ wherein ₃Be the scattering coefficient vector of optimizing.

2. method according to claim 1, wherein the described orthogonal matching pursuit OMP method of utilizing of step 3 is found the solution suc as formula＜3〉0 norm optimization problem, carry out as follows:

3a) input dictionary

3b) initialization is about to signal margin r and is initialized as frequency domain observation signal matrix column vector s, and scattering coefficient vector σ is initialized as 0, and atom index vector a is initialized as sky, establishes primary iteration number of times k=1, and the beginning iteration;

3c) the related coefficient of Dictionary of Computing and signal margin r vector C

$C=D_0{(x,y,L|{\widehat{\mathrm{\&theta;}}}_0)}^H\&CenterDot;r---<8>$

Wherein () ^HThe expression conjugate transpose, the sequence number of greatest member is a among the related coefficient vector C _k, can get atom index vector a and be:

a＝[a ₁，...,a _k] <9>

3d) utilize least square method calculation method for scattering coefficient vector σ

Wherein The expression pseudoinverse, D ₀(:, a) be dictionary D ₀Middle row number are a _iThe matrix i=1 that consists of of k column vector ..., k, k are the current iteration number of times;

Upgrade surplus r:

r=s-D ₀(:,a)·σ(a) <11>

Wherein σ (a) is a for sequence number among the scattering coefficient vector σ _iThe column vector i=1 that consists of of k element ..., k;

3e) calculate reconstruct energy Ratios η _k

${\mathrm{\&eta;}}_k=\frac{\mathrm{\&Sigma;}{\left|\right|s_k\left|\right|}_2^2}{\mathrm{\&Sigma;}{\left|\right|s\left|\right|}_2^2}---<12>$

s _k＝D ₀(:,a)·σ(a)

S wherein _kBe reconstruction signal,

Represent 2 norms square;

If 3f) η _k-η _K-1≤ δ stops iteration, and wherein δ is the thresholding of the difference of adjacent iteration energy Ratios, gets δ=0.001; Otherwise k=k+1 also goes to step 3c).

3. method according to claim 1, wherein the described orthogonal matching pursuit OMP method of utilizing of step 5 is found the solution suc as formula＜5〉0 norm optimization problem, carry out as follows:

5a) input dictionary

5b) initialization is about to signal margin r and is initialized as frequency domain observation signal matrix column vector s, and scattering coefficient vector σ is initialized as 0, and atom index vector a is initialized as sky, establishes primary iteration number of times k=1, and the beginning iteration;

5c) the related coefficient of Dictionary of Computing and signal margin r vector C

$C=D_1{(L,\stackrel{\&OverBar;}{\mathrm{\&phi;}}|{\widehat{\mathrm{\&theta;}}}_1)}^H\&CenterDot;r---<13>$

Wherein () ^HThe expression conjugate transpose, the sequence number of greatest member is a among the related coefficient vector C _k, can get atom index vector a and be:

a＝[a ₁，...,a _k] <14>

5d) utilize least square method calculation method for scattering coefficient vector σ

Wherein

The expression pseudoinverse, D ₁(:, a) be dictionary D ₁Middle row number are a _iThe matrix i=1 that consists of of k column vector ..., k, k are the current iteration number of times;

Upgrade surplus r:

r=s-D ₁(:,a)·σ(a) <16>

Wherein σ (a) is a for sequence number among the scattering coefficient vector σ _iThe column vector i=1 that consists of of k element ..., k;

5e) calculate reconstruct energy Ratios η _k

${\mathrm{\&eta;}}_k=\frac{\mathrm{\&Sigma;}{\left|\right|s_k\left|\right|}_2^2}{\mathrm{\&Sigma;}{\left|\right|s\left|\right|}_2^2}---<17>$

s _k＝D ₁(:,a)·σ(a)

S wherein _kBe reconstruction signal,

Represent 2 norms square;

If 5f) η _k-η _K-1≤ δ stops iteration, and wherein δ is the thresholding of the difference of adjacent iteration energy Ratios, gets δ=0.001; Otherwise k=k+1 also goes to step 5c).

4. method according to claim 1, wherein the described orthogonal matching pursuit OMP method of utilizing of step 7 is found the solution suc as formula＜7〉0 norm optimization problem, carry out as follows:

7a) input dictionary

7b) initialization is about to signal margin r and is initialized as frequency domain observation signal matrix column vector s, and scattering coefficient vector σ is initialized as 0, and atom index vector a is initialized as sky, establishes primary iteration number of times k=1, and the beginning iteration;

7c) the related coefficient of Dictionary of Computing and signal margin r vector C

$C=D_2{(x,y,L|{\widehat{\mathrm{\&theta;}}}_2)}^H\&CenterDot;r---<18>$

Wherein () ^HThe expression conjugate transpose, the sequence number of greatest member is a among the related coefficient vector C _k, obtain atom index vector a and be:

a＝[a ₁，...,a _k] <19>

7d) utilize least square method calculation method for scattering coefficient vector σ

Wherein

The expression pseudoinverse, D ₂(:, a) be dictionary D ₂Middle row number are a _iThe matrix i=1 that consists of of k column vector ..., k, k are the current iteration number of times;

Upgrade surplus r:

r=s-D ₂(:,a)·σ(a) <21>

Wherein σ (a) is a for sequence number among the scattering coefficient vector σ _iThe column vector i=1 that consists of of k element ..., k;

7e) calculate reconstruct energy Ratios η _k:

${\mathrm{\&eta;}}_k=\frac{\mathrm{\&Sigma;}{\left|\right|s_k\left|\right|}_2^2}{\mathrm{\&Sigma;}{\left|\right|s\left|\right|}_2^2}---<22>$

s _k＝D ₂(:,a)·σ(a)

S wherein _kBe reconstruction signal,

Represent 2 norms square;

If 7f) η _k-η _K-1≤ δ stops iteration, and wherein δ is the thresholding of the difference of adjacent iteration energy Ratios, gets δ=0.001; Otherwise k=k+1 also goes to step 7c).

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